Question

Determine which statement is true. A) t || u and v || w B) t || w and u || v C) t || v and u || w D) t || u and u || v

Answer 1

the answer is c

Answer 2

Option C) is correct

Explanation:

Consider the attached figure:

As
`\angle 1` and
`120^(\circ)` form a linear pair,

`\angle 1+120^(\circ)=180^(\circ)\\\angle 1=180^(\circ)-120^(\circ)\\=60^(\circ)`

`\angle 1=\angle 2=60^(\circ)` and
`\angle 1 , \angle 2` form a pair of corresponding angles, so
`t||v`

( we know that if corresponding angles are equal , lines are parallel )

Also, as
`\angle 3\,,\,110^(\circ)` form a linear pair, so

`110^(\circ)+\angle 3=180^(\circ)\\\angle 3=180^(\circ)-110^(\circ)\\=70^(\circ)`

Now as
`\angle 3=\angle 4=70^(\circ)` and
`\angle 3\,,\,\angle 4` form a pair of alternate interior angles, so
`u||w`

So, option C) is correct